Geometric Group Theory Seminar
Title: Maximal subgroups, weakly maximal subgroups and generalisations
Speaker: Paul-Henry Leemann
University: Xi’an Jiaotong-Liverpool University
Time: May 23, Friday 10 am (China Standard Time).
Venue: Gewu Building, 315
Zoom ID: 989 8689 0777 (Password: 527147)
Link: https://zoom.us/j/98986890777?pwd=bqbSH2abTPwqkzbDNr6E7YoH77gzXI.1
Abstract:
One of the numerous approaches to study a group G is to study its lattice of subgroups. In this setting it is natural to start with the study of the maximal subgroups. A first question is whether G has maximal subgroups of infinite index. The next step is to study weakly maximal subgroups of G, that is subgroups that are maximal among infinite index subgroups. This class contains all maximal subgroups of infinite index, but it is not restricted to them. With my collaborators D. Francoeur and T. Nagnibeda, we looked at the following generalisation: subgroups that are maximal in their commensurability class (max-com).
The talk will be self-contained and will start with a brief historical introduction and some easy examples. I will then explain how max-com subgroups are linked to irreducible representations. Finally, I will present a beginning of a classification of max-com subgroups for groups with a micro-supported action (as branch groups or Thompson’s groups).
